Gravitation 4 Question 3
4. If the distance between the earth and the sun were half its present value, the number of days in a year would have been
(a) 64.5
(b) 129
(c) 182.5
(d) 730
(1996, 2M)
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Answer:
Correct Answer: 4. (b)
Solution:
- From Kepler’s third law $T^{2} \propto r^{3}$ or $T \propto(r)^{3 / 2}$
$$ \begin{gathered} \therefore \quad \frac{T _2}{T _1}={\frac{r _2}{r _1}}^{3 / 2} \quad \text { or } \quad T _2=T _1{\frac{r _2}{r _1}}^{3 / 2}=(365) \frac{1}{2}^{3 / 2} \\ \Rightarrow \quad T _2 \approx 129 \text { days } \end{gathered} $$
